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Unification of nonlinear filtering in the context of binary logical calculus, part I: Binary filters

✍ Scribed by Edward R. Dougherty; Robert M. Haralick

Publisher: Springer US
Year: 1992
Tongue: English
Weight: 891 KB
Volume: 2
Category: Article
ISSN: 0924-9907
DOI: 10.1007/bf00118588

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✦ Synopsis

The mathematical structure of nonlinear filtering is expressed in the context of binary logic. This first part of a two-part study concerns the binary setting. Operator properties, such as antiextensivity and idempotence, are expressed in finite logical expressions, as are the Matheron representation for morphological filters and its extension to translation-invariant operators, thereby giving simplicity to both operational properties and representations and also exposing the manner in which logic methods can be used for filter design and analysis. The second part of the study treats gray-scale filters.

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Unification of nonlinear filtering in the context of binary logical calculus, part II: Gray-scale filters

✍ Edward R. Dougherty 📂 Article 📅 1992 🏛 Springer US 🌐 English ⚖ 639 KB

This second part of a two-part study concerning the logical structure of nonlinear filters treats gray-scale filters. The algebraic framework of threshold decomposition is dedscribed in terms of the appropriate underlying commuting diagram, along with the manner in which generalized stack filters fa